The fast bowler has a "serious" ankle ligament damage and his WC availability will not be known for at least a week, Cricket Australia said.

Australian fast bowler Brett Lee has a "serious" ankle ligament damage and his World Cup availability will not be known for at least a week, Cricket Australia said after he was flown home on Friday.

But Lee does not need surgery after injuring his left ankle in training for the Chappell-Hadlee Trophy one-day series in New Zealand, the governing body said in a statement.

"Brett has suffered a serious ligament injury to his left ankle. He was seen by an orthopaedic surgeon who decided that he does not require surgery and will be initially managed with crutches and a brace," said team physiotherapist Alex Kountouris.

"The surgeon will review him in a week's time and assess his prospects of playing in the World Cup.

"It is difficult to put an exact time on his recovery at this early stage. This should become clearer in the next seven-10 days."

Lee said he feared for the worst when he first went down on the ankle but was relieved not to need an operation.

"The good news is that I don't need an operation. There are torn ligaments in my left ankle and yesterday I was in a lot of pain," he said.

"When I went down I heard a crack in my ankle and things weren't looking good.

"After consulting with the doctor today I am more positive, but it's too hard to say what the outcome will be.

"I'll be doing everything I can to make sure I have a chance of playing at the World Cup" he said.